Khintchine types of translated coordinate hyperplanes

• Autorzy: Felipe A. Ramírez
• Języki publikacji: EN

Abstrakty

EN

There has been great interest in developing a theory of "Khintchine types" for manifolds embedded in Euclidean space, and considerable progress has been made for curved manifolds. We treat the case of translates of coordinate hyperplanes, decidedly flat manifolds. In our main results, we fix the value of one coordinate in Euclidean space and describe the set of points in the fiber over that fixed coordinate that are rationally approximable at a given rate. We identify translated coordinate hyperplanes for which there is a dichotomy as in Khintchine's Theorem: the set of rationally approximable points is null or full, according to the convergence or divergence of the series associated to the desired rate of approximation.

Kategorie tematyczne

• 11K50: Metric theory of continued fractions
• 11K60: Diophantine approximation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 170
• Numer: 3
• Strony: 243-273

Daty

wydano

2015

Twórcy

autor

Felipe A. Ramírez

• Department of Mathematics, University of York, Heslington, York, UK
• Department of Mathematics and Computer Science, Wesleyan University, 265 Church Street, Middletown, CT 06459, U.S.A.

Identyfikatory

DOI

10.4064/aa170-3-3